A physics-based explanation for the existence of Stokes drift

The particle trajectories in irrotational, incompressible, inviscid deep-water surface gravity waves are open, leading to a net drift in the direction of wave propagation known as the Stokes Drift. This is responsible for catalysing surface wave-induced mixing in the ocean, and is essential to the transport of marine debris and generation of Langmuir circulation.

Despite its discovery in 1847 by George Gabriel Stokes, the current explanations for Stokes drift are ambiguous and obscure the fundamental underlying kinematic nature of this phenomenon, one that is dominated by vorticity even when the flow is irrotational.

Through calculations in the Lagrangian reference frame, the most natural frame for understanding particle trajectories, we highlight the connection between the vorticity and the wave-induced drift. From our direct analysis in the Lagrangian frame, we provide clearer definitions of quantities such as `wave phase, crest, and trough' and call into question common explanations such as `the particle spends more time at the crest of the wave vs. the trough'. The results are further validated through numerical simulations of particle trajectories from our newly developed surface wave solver.